

A046107


Triangle of prime numbers in which nth row lists all primes p such that 1/p has decimal period n, n >= 1.


13



3, 11, 37, 101, 41, 271, 7, 13, 239, 4649, 73, 137, 333667, 9091, 21649, 513239, 9901, 53, 79, 265371653, 909091, 31, 2906161, 17, 5882353, 2071723, 5363222357, 19, 52579, 1111111111111111111, 3541, 27961, 43, 1933, 10838689, 23, 4093
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OFFSET

1,1


COMMENTS

The number of numbers in each row n is given by A112505(n).
In the 18th century, the Japanese mathematician Ajima Naonobu (aka Ajima Chokuyen) gave the terms through 5882353 (Smith and Mikami, p. 199).  Jonathan Sondow, May 25 2013


REFERENCES

Ajima Naonobu (aka Ajima Chokuyen), Fujin IsshÅ© (Periods of Decimal Fractions).


LINKS

Ray Chandler, Rows n=1..322, flattened (first 276 rows from T. D. Noe)
David Eugene Smith and Yoshio Mikami, A History of Japanese Mathematics, Open Court, Chicago, 1914; chapter X.
Eric Weisstein's World of Mathematics, Decimal Expansion.
Index entries for sequences related to decimal expansion of 1/n


EXAMPLE

First rows of irregular triangle are:
3;
11;
37;
101;
41, 271;
7, 13;
239, 4649;
73, 137;
333667;
9091;
21649, 513239;
9901;
53, 79, 265371653;
909091;
31, 2906161;
17, 5882353;
...


MATHEMATICA

pp={}; Do[f=Transpose[FactorInteger[10^n1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Print[p], {n, 66}] (* T. D. Noe, Sep 08 2005 *)


CROSSREFS

Cf. A007138 (first column).
Sequence in context: A095088 A306362 A007138 * A243110 A061075 A005422
Adjacent sequences: A046104 A046105 A046106 * A046108 A046109 A046110


KEYWORD

nonn,tabf,base


AUTHOR

Eric W. Weisstein


STATUS

approved



